When has Trump ever bothered trying to create plausible deniability? He's repeatedly been confronted about his past bad behavior and outrageous statements. His response is always either to deny that it happened--often despite video evidence contradicting him--or to claim that the accuser is misrepresenting him. Why would he suddenly change his tactics here, and why wait three months to do so?
Consider that your interpretation requires Trump to be one extremely dumb but lucky bastard. He's so stupid that he doesn't realize that mocking a physical disability will piss off practically everybody. Luckily for him, he's also too incompetent to simply bend his elbow and wrist and hold them close to his body. He instead flails around wildly, makes faces, and changes his voice, none of which bear any resemblance to Kovaleski's arthrogryposis. After the public backlash, he takes advantage of his own gross incompetence and claims that he wasn't mocking arthrogryposis, but was simply doing a "flustered reporter" impression. He then waits months and does the same to Ted Cruz to build further credibility in his story. Seems unlikely, IMO.